# Questions tagged [plane-geometry]

Plane Geometry is about flat shapes like lines, circles and triangles , shapes that can be drawn on a piece of paper

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### Curves of constant width that contain triangles

Wikipedia references: Curve of constant width, Reuleaux polygon. We record a pair of questions on the same lines as Smallest 3-ellipses that contain triangles. Questions: How does one find and ...
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### Smallest 3-ellipses that contain triangles

Reference: https://en.wikipedia.org/wiki/N-ellipse Question: How does one find and characterize the smallest 3-ellipses (n-ellipses with n =3) that contain a given triangle? 'Smallest' can mean 'least ...
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### Pseudo-Droz-Farny circles

I would like to present a construction of 2 circles. These 2 circles are somewhat similar in appearance to the well known Droz-Farny circles that can be drawn for every isogonal conjugate pairs of ...
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### Is the derivative the unique operation on points in the plane that preserves convexity?

Let $C(n)$ be the space of multisets of size $n$ of points in the Euclidean plane, topologised appropriately, and consider a surjective continuous map: $$D:C(n)\rightarrow C(n-1)$$ Such that the ...
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I made some rookie attempt to define the 4th Lemoine circle recently. The alternative name for this circle was suggested yesterday. Further investigation revealed a family of circles associated with ...
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### Tiling a Jordan polygon

I saw this problem some years ago, don't remember the source: Let $P$ be a Jordan polygon (i.e. the only points of the plane belonging to two edges are the polygon vertices) that can be tiled with ...
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### Cutting convex polygons into triangles of same diameter

This question continues from: Cutting convex regions into equal diameter and equal least width pieces Definitions: The diameter of a convex region is the greatest distance between any pair of points ...
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Can you prove the following claim: Claim. Given hexagon circumscribed about an ellipse. Let $A_1,A_2,A_3,A_4,A_5,A_6$ be the vertices of the hexagon and let $B$ be the intersection point of its ...